Polynomial predistorter using complex vector multiplication

ABSTRACT

A polynomial predistorter and predistorting method for predistorting a complex modulated baseband signal are provided. In the polynomial predistorter, a first complex multiplier generates first complex predistortion gains, using a current input signal and complex polynomial coefficients modeled on the inverse non-linear distortion characteristic of the power amplifier, and multiplies them by I and Q signal components of the current input signal, respectively. At least one second complex multiplier generates second complex predistortion gains using the complex polynomial coefficients and previous predistorted signals and multiplies them by I and Q signal components of the previous predistorted signals, respectively. A summer sums the outputs of the first and second complex multipliers and outputs the sum as a predistorted signal to the power amplifier.

PRIORITY

[0001] This application claims priority under 35 U.S.C. § 119 to anapplication entitled “Polynomial Predistorter Using Complex VectorMultiplication” filed in the Korean Intellectual Property Office on Feb.6, 2003 and assigned Serial No. 2003-7603, the contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates generally to wideband poweramplification, and in particular, to a predistorter and predistortingmethod for linearizing the non-linear distortion characteristic of acomplex modulated baseband signal, caused by a power amplifier.

[0004] 2. Description of the Related Art

[0005] In a typical mobile communication system that communicates viaradio frequency (RF) signals, RF amplifiers are categorized as beinglow-power, low-noise receive amplifiers or high-power transmitamplifiers (HPA). The efficiency of the high-power transmit amplifier isa greater consideration than noise. The high-power amplifier is widelyused in mobile communication applications and operates near a non-linearoperation point to achieve high efficiency.

[0006] Intermodulation distortion (IMD) from the amplifier outputadversely affects out of band frequencies as well as in band frequencieswith spurious signals. A feed forward method is usually adopted toeliminate the spurious component. Despite the advantage of perfectelimination of the spurious component, however, the feed forward methodhas low amplification efficiency and requires control at an RF stage.Therefore, the HPA becomes bulky and increases system cost.

[0007] Digital predistortion (DPD) is being studied as a means ofproviding high efficiency and low cost in the mobile communicationindustry. The DPD precompensates an input signal with an inverse of thenon-linearity of a power amplifier at a digital stage and renders theamplifier output linear. The non-linearity of the power amplifier showsup as Amplitude Modulation to Amplitude Modulation (AM to AM) conversiondistortion and Amplitude Modulation to Phase Modulation (AM to PM)conversion distortion. The AM to AM conversion distortion is defined asa change in the amplitude of an output signal compared to the amplitudeof an input signal, while the AM to PM conversion distortion is definedas a change in the phase of the output signal compared to the amplitudeof the input signal.

[0008] Most predistorters apply to single tone frequency signals ornarrow band frequency signals. Therefore, they generally compensate forthe memoryless non-linearity of a power amplifier. The memorylessnon-linearity refers to the present output being influenced by thepresent input only. However, the memoryless non-linearity of thenon-linear amplifier at a wideband frequency causes previous inputsignals as well as the present input signal to affect the presentamplifier output, thereby substantially changing the AM to AM and AM toPM characteristics. This phenomenon is called memory effects. Thenon-linearity of a power amplifier varies with the frequency bandwidthof an input signal.

[0009] The increasing use of wideband frequencies in mobilecommunication systems has motivated research and development on thememoryless effects of non-linear amplifiers. A main technique ofcompensating for both the memoryless non-linearity and memory effects ofa non-linear amplifier applies a simplified Volterra model. A Volterraseries can be seen as a Taylor series with a memory. The Volterra seriesis used to accurately model a non-linear system. A Volterra modelpredistorter eliminates the non-linearity of a non-linear amplifierusing an inverse of a Volterra series model that accurately simulatesthe non-linearity.

[0010] For the Volterra model, the predistortion characteristic tolinearize a power amplifier with a memory is expressed as a discreteVolterra series with a finite memory. A signal d(n) predistorted bymodifying the discrete Volterra series to a finite discrete Volterraseries is represented by

d(n)=h _(volterra)(n)EX _(volterra)(n)   (1)

[0011] And a Volterra kernel vector h_(volterra) and an input signalvector x_(volterra) are given as

h _(volterra)(n)=[h ₁(0),h ₁(1),h ₁(2), . . . ,h ₁(m−1),h ₃(0,0),h₃(0,1),h ₃(0,2), . . . ,h ₃(0,m−1), . . . , h ₃(1,0),h ₃(1,1),h ₃(1,2),. . . ,h ₃(1,m−1), . . . ,h ₃(m−1,m−1)]x _(volterra)(n)=[x(n), x(n−1),x(n−2), . . . , x(n−m−1), x(n)|x(n)|, x(n−1)|x(n)|² , x(n−2)|x(n)|² ,x(n−m−1)|x(n)|² , x(n)|x(n−1)|² , x(n−1)|x(n−1)|² , . . .,x(n−m−1)|x(n)|² , x(n)|x(n−1)|² ,x(n−−1)|x(n−1)|² , . . .,x(n−m−1)|x(n−1)|² , . . . ,x(n−m−1)|x(n−m−1|²]^(T)   (2)

[0012] where h_(i)(m,n) is the complex predistortion gain for anith-order signal, that is, the gain of mth and nth previous input signalsamples in combination. As noted, this predistorter is configured in anFinite Impulse Response (FIR) structure and considers previous inputsignal samples up to an mth one.

[0013] The predistorter generates the predistorted signal d(n) bymultiplying a complex input signal by the complex gain. After the signalis amplified in an HPA, the signal d(n) is linearized. By separating theVolterra kernel vector h_(volterra) and the input signal vectorx_(volterra) into in-phase (I) signal components and quadrature-phase(Q) signal components, multiplication in the predistorter is expressedas

(A+jB)(p+jq)=Ap−Bq+j(Aq+Bp)  (3)

[0014] where A and B denote the I and Q signal components of an inputsignal, respectively, and p and q denote I and Q predistortion gainsextracted by an adaptation algorithm, respectively.

[0015] As noted from Eq. (3), the predistorter using the discreteVolterra series experiences a rapid increase in computation volume witha modulation order. Moreover, if an input signal vector is formed fromprevious (m31 1) values and applied to the input of a power amplifierinfluenced by m_(PA) finite memory samples, the number of previous inputsignal samples that affect the power amplifier is m_(PA)+m−1. Thus, thepower amplifier is affected by more memory samples than the predistorterand the predistorter fails to appropriately linearize the non-linearityof the power amplifier. This is attributed to lack of sufficientinformation required to generate a predistorted signal in thepredistorter.

[0016] Despite different distortions in the I and Q signals of theamplifier output, the same predistortion gain is multiplied by the I andQ signals, thereby limiting predistortion gains. Therefore, errors mayoccur in the predistortion signal for linearizing the power amplifierand full linearization cannot be achieved.

SUMMARY OF THE INVENTION

[0017] An object of the present invention is to substantially solve atleast the above problems and/or disadvantages and to provide at leastthe advantages below. Accordingly, an object of the present invention isto provide a predistorter using a more simplified complex polynomial.

[0018] Another object of the present invention is to provide apolynomial predistorter using an indirect training architecture.

[0019] A further object of the present invention is to provide apredistorter of an Infinite Impulse Response (IIR) structure, forgenerating a predistortion signal using a previous output signal insteadof a previous input signal.

[0020] Still another object of the present invention is to provide apredistorter for compensating for the non-linearity of a power amplifierby multiplying the I and Q signal components of an input signal bycorrespondingly different predistortion gains.

[0021] The above objects are achieved by a polynomial predistorter andpredistorting method for predistorting a complex modulated basebandsignal, providing the predistorted signal to a power amplifier, andcompensating for the non-linear distortion characteristic of the poweramplifier using complex vector multiplication. In the polynomialpredistorter, a first complex multiplier generates first complexpredistortion gains using a current input signal and complex polynomialcoefficients, for I and Q signal predistortion, and multiplies the firstcomplex predistortion gains by I and Q signal components of the currentinput signal, respectively. Here, the complex polynomial coefficientsare modeled on the inverse non-linear distortion characteristic of thepower amplifier. At least one second complex multiplier generates secondcomplex predistortion gains using the complex polynomial coefficientsand previous predistorted signals corresponding to the complexpolynomial coefficients, for I and Q signal predistortion, andmultiplies the second complex predistortion gains by I and Q signalcomponents of the previous predistorted signals, respectively. A summergenerates a predistorted signal by summing the outputs of the first andsecond complex multipliers and outputs the predistorted signal to thepower amplifier.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The above and other objects, features and advantages of thepresent invention will become more apparent from the following detaileddescription when taken in conjunction with the accompanying drawings inwhich:

[0023]FIG. 1 is a block diagram illustrating a transmitter foroutputting a linearized amplified signal by use of polynomialpredistorters according to an embodiment of the present invention;

[0024]FIG. 2 is a block diagram illustrating a first predistorterillustrated in FIG. 1, for outputting a first predistortion signal d(n)for the input of a signal x(n) according to an embodiment of the presentinvention;

[0025]FIG. 3 is a detailed view illustrating a first complex multiplieraccording to an embodiment of the present invention; and

[0026]FIG. 4 is a detailed view illustrating a second predistorteraccording to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0027] An embodiment of the present invention will be described hereinbelow with reference to the accompanying drawings. In the followingdescription, well-known functions or constructions are omitted forconciseness.

[0028] In accordance with an embodiment of the present invention, apredistorted signal is generated using a current input signal andprevious predistorted signals. Predistortion gains, which are multipliedby the current input signal and the previous predistorted signals forgeneration of the predistorted signal, are achieved through indirecttraining.

[0029]FIG. 1 illustrates a transmitter that outputs a linearizedamplified signal by use of polynomial predistorters based on an indirecttraining architecture according to an embodiment of the presentinvention.

[0030] Referring to FIG. 1, the transmitter includes two predistorters100 and 200 which use the same predistortion polynomial coefficients toestimate the non-linear distortion characteristic of a power amplifier300.

[0031] When necessary, an error correction circuit for correcting gainand phase errors possibly generated from an analog quadrature modulator,a Direct Current (DC) offset cancellation circuit for eliminatingleakage power, a digital quadrature modulator, a digital to analogconverter, a band pass filter, and a frequency upconverter can beinserted between the first predistorter 100 and the power amplifier 300.Also, a frequency downconverter, a band pass filter, an analog todigital converter, and a digital quadrature demodulator can be insertedbetween the power amplifier 300 and the second predistorter 200. Sincethe above components are not characteristic of the embodiment of thepresent invention, they are not shown here.

[0032] The first predistorter 100 provides an input complex modulatedbaseband signal x(n) and a first predistorted signal d(n) to the poweramplifier 300. d(n) is a signal predistorted by means of polynomialcoefficients modeled on the inverse non-linear distortion characteristicof the power amplifier 300. An amplified signal y(n) output from thepower amplifier 300 is provided to the second predistorter 200.

[0033] The second predistorter 200 outputs a second predistorted signalo(n) resulting from predistorting y(n) by means of the same polynomialcoefficients as those for the first predistorter 100. It is ideal thatthe second predistorter 200 outputs the same signal as the firstpredistorted signal for the input of y(n). For this purpose, an errorcalculator 310 generates an error signal e(n) by subtracting o(n) fromd(n) and the second predistorter 200 updates the polynomial coefficientsby a known adaptation algorithm such that the power or magnitude of e(n)is minimized. The updated polynomial coefficients are applied to thefirst predistorter 100.

[0034] Thus, the first and second predistorters 100 and 200 operatebased on the updated polynomial coefficients, and as the updating isrepeated, the output of the power amplifier 300 is gradually linearized.

[0035] The first and second predistorters 100 and 200 outputpredistorted signals using a current input signal and previouspredistorted signals.

[0036]FIG. 2 illustrates the first predistorter 100 that outputs thefirst predistorted signal d(n) for the input of the signal x(n)according to an embodiment of the present invention. The firstpredistorter 100 is assumed to use two previous predistorted signalsamples. The structure and operation of the first predistorter 100 asdescribed below are also applied to the second predistorter 200.

[0037] Referring to FIG. 2, a first complex multiplier 110 multipliesthe I and Q signal components of x(n) by corresponding predistortiongains. The outputs of the first complex multiplier 110 are combined withthe outputs of second and third complex multipliers 120 and 130, therebyproducing the first predistorted signal d(n). The second complexmultiplier 120 multiplies a signal d(n−1) obtained by delaying d(n) onesample time in a delay 154 by corresponding predistortion gains. Thethird complex multiplier 130 multiplies a signal d(n−2) obtained bydelaying d(n) two sample times in delays 154 and 156 by correspondingpredistortion gains.

[0038] A summer 140 sums the I and Q outputs of the first, second andthird complex multipliers 110, 120 and 130 at I component adders 142 and146 and at Q component adders 144 and 148. A multiplier 152 shifts the Qsignal component sum by 90° and an adder 150 adds the shifted Q signalcomponent to the I signal component sum, thus outputting the firstpredistorted signal d(n).

[0039]FIG. 3 illustrates the first complex multiplier 110 in detail, asa representative of the complex multipliers 110, 120 and 130 accordingto an embodiment of the present invention. Referring to FIG. 3, thefirst complex multiplier 110 detects the I signal component Re{x(n)} ofx(n) through a real number detector 112 a and the Q signal componentIm{x(n)} of x(n) through an imaginary number detector 112 b. Thedetected signal components are fed to four multipliers 114 a to 114 d.

[0040] The first complex multiplier 110 detects the magnitude 1x(n)1 ofx(n) through an absolute value calculator 118 a. A polynomial calculator118 b generates I predistortion gains p and q and Q predistortion gainsr and s by calculating a predistortion polynomial using 1x(n)1 andcomplex polynomial coefficients c_(i) and c_(q) calculated by indirecttraining in the second predistorter 200.

[0041] The multipliers 114 a and 114 b multiply Re{x(n)} by p and r andthe multipliers 114 c and 114 d multiply Im{x(n)} by q and s. That is, pand r are predistortion gains for the I signal component of x(n), whileq and s are predistortion gains for the Q signal component of x(n). Anadder 116 a adds the outputs of the multipliers 114 a and 114 c andoutputs the sum as the I signal component, and an adder 116 b adds theoutputs of the multipliers 114 b and 114 d and outputs the sum as the Qsignal component.

[0042] In the same manner, the second and third complex multipliers 120and 130 generate predistortion gains by calculating a predistortionpolynomial using input signal magnitudes 1d(n−1)1 and 1d(n−2)1 and thesame complex polynomial coefficients and multiply the predistortiongains by the I and Q signal components of the input signals d(n−1) andd(n−2).

[0043] Compared to conventional technology, the predistortion of aninput signal in the predistortion structure configured as illustrated inFIGS. 2 and 3 is expressed as

[A B A B][p q jr js] ^(T) =Ap+Bq+j(Ar+Bs)  (4)

[0044] where A and B denote the I and Q signal components of the inputsignal, respectively and p, q, r and s denote I and Q predistortiongains extracted by the adaptation algorithm. As stated before, p and rare I and Q predistortion gains by which the I signal component, A ofthe input signal is predistorted, while q and s are I and Qpredistortion gains by which the Q signal component, B of the inputsignal is predistorted.

[0045] These predistortion gains are achieved by calculating thepredistortion polynomial using the complex polynomial coefficientsobtained by indirect training. As is known, the indirect training is ascheme of realizing linearization without knowledge of thecharacteristic model of a power amplifier, and polynomial coefficientsfor compensating for the non-linearity of the power amplifier arecomputed by the adaptation algorithm. Now, a description will be made ofthe predistortion according to the embodiment of the present invention,taking the first predistorter 100 illustrated in FIG. 1 as an example.

[0046] The predistorted signal d(n) is

d(n)=d _(i)(n)+jd _(q)(n)=x(n)E(c _(i) +jc _(q))  (5)

[0047] where n is the time index of a sample unit and ci and c_(q) arethe respective I and Q signal components of a complex polynomialcoefficient for the input signal x(n).

[0048] Using a P-order polynomial and previous samples before up to anMth sample time, the input signal x(n) and the complex polynomialcoefficients are given in the form of matrices as follows.

x(n)=[x _(i)(n),x _(q)(n), x _(i)(n)|x(n)|,x _(q)(n)|x(n)|, . . . , x_(i)(n)|x(n)|^(P−1) , x _(q)(n)|x(n)|^(P−1) , d _(i)(n−1),d _(q)(n−1),d_(i)(n−1)|d(n−1)|,d _(q)(n−1)|d(n−1)|, . . . , d _(i)(n−1)|d(n−1)|^(P−1),d _(q)(n−1)|d(n−1)|^(P−1) , d _(i)(n−M),d _(q)(n−M),d_(i)(n−M)|d(n−M)|,d _(q)(n−M)|d(n−M)|, . . . , d _(i)(n−M)|d(n−M)|^(P−1),d _(q)(n−M)|d(n−M)|^(P−1)]

c _(i) =[c _(ii,0,0) ,c _(iq,0,0) , . . . ,c _(ii,0,(P−1)) ,c_(iq,0,(P−1)) ,c _(ii,1,0) ,c _(iq,1,0) , . . . ,c _(ii,1,(P−1)) ,c_(iq,1,(P−1)) , . . . , c _(ii,M,0) ,c _(iq,M,0) , . . . ,c_(ii,M,(P−1)) ,c _(iq,M,(P−1))]^(T)

c _(q) =[c _(qi,0,0) ,c _(qq,0,0) , . . . ,c _(qi,0,(P−1)) ,c_(qq,0,(P−1)) ,c _(qi,1,0) ,c _(qq,1,0) , . . . ,c _(qi,1,(P−1)) ,c_(qq,1,(P−1)) , . . . , c _(qi,M,0) ,c _(qq,M,0) , . . . ,c_(qi,M,(P−1)) ,c _(qq,M,(P−1))]^(T)   (6)

[0049] where [ ]^(T) denotes predistortion matrix. Then, thepredistortion gains are computed in the polynomial calculator 118 b by

p=c _(ii,0,0) +c _(ii,0,1) |x(n)|+ . . . +c _(ii,0,(P−1)) |x(n)|^((P−1))

q=c _(iq,0,0) +c _(iq,0,1) |x(n)|+ . . . +c _(iq,0,(P−1)) |x(n)|^((P−1))

r=c _(qi,0,0) +c _(qi,0,1) |x(n)|+ . . . +c _(qi,0,(P−1)) |x(n)|^((P−1))

s=c _(qq,0,0) +c _(qq,0,1) |x(n)|+ . . . +c _(qq,0,(P−1))|x(n)|^((P−1))  (7)

[0050] Although Eq. (7) represents the predistortion gains for the inputsignal x(n), it can represent in the same manner predistortion gainsc_(ii,m,(0˜P−1),) c_(iq,m,(0˜P−1), c) _(qi,m,(0˜P−1)), c_(qq,m,(0˜P−1))for a previous mth predistorted signal d(n-m).

[0051]FIG. 4 illustrates the second predistorter 200 illustrated in FIG.1 in detail according to an embodiment of the present invention. Asillustrated, a first complex multiplier 210 multiplies the current inputsignal y(n) (interchangeably expressed as y_(n)) by correspondingpredistortion gains. The outputs of the first complex multiplier 210 arecombined with the outputs of second and third complex multipliers 220and 230, thereby producing the second predistorted signal o(n)(interchangeably expressed o_(n)). The second complex multiplier 220multiplies a signal y(n−1) obtained by delaying y(n) one sample time ina delay 254 by corresponding predistortion gains. The third complexmultiplier 230 multiplies a signal y(n−2) obtained by delaying y(n) twosample times in delays 254 and 256 by corresponding predistortion gains.

[0052] A summer 240 sums the I and Q outputs of the first, second andthird complex multipliers 210, 220 and 230, shifts the Q signalcomponent sum by 90°, and adds the shifted Q signal component to the Isignal component sum, thus outputting the second predistorted signalo_(n).

[0053] The second predistorted signal o(n) is

o(n)=o _(i)(n)+jo _(q)(n)=y(n)E(c _(i) +jc _(q))  (8)

[0054] where c_(i) and c_(q) are the respective I and Q signalcomponents of a complex polynomial coefficient for the input signalo(n).

[0055] Using a P-order polynomial and previous samples before up to anMth sample time, the amplified signal x(n) input to the secondpredistorter 200 is

y(n)=[y _(i)(n),y _(q)(n), y _(i)(n)|y(n)|,y _(q)(n)|y(n)|, . . . , y_(i)(n)|y(n)|^(P−1) , y _(q)(n)|y(n)|^(P−1) , o _(i)(n−1),o _(q)(n−1),o_(i)(n−1)|o(n−1)|,o _(q)(n−1)|o(n−1)|, . . . , o _(i)(n−1)|o(n−1)|^(P−1),o _(q)(n−1)|o(n−1)|^(P−1) , o _(i)(n−M),o _(q)(n−M),o_(i)(n−M)|o(n−M)|,o _(q)(n−M)|o(n−M)|, . . . , o _(i)(n−M)|o(n−M)|^(P−1),o _(q)(n−M)|o(n−M)|^(P−1)]  (9)

[0056] Referring to FIG. 4, a digital signaling processor (DSP) 260calculates polynomial coefficients c_(ii), c_(iq), c_(qi) and c_(qq)using a known adaptation algorithm such as Recursive Least Square (RLS)or Least Mean Square (LMS), such that an error signal e(n)=d(n)-o(n) isminimized. The polynomial coefficients are formed as illustrated in Eq.(6). These polynomial coefficients are provided to the polynomialcalculator 118 b of the first predistorter 100. To do so, a samplememory 264 stores y(n) and previous samples of o(n) before up to an Mthsample time received from a multiplexer 262 and provides them to thedigital signaling processor 260. The sample memory 264 has a capacity ofstoring (M+1) samples.

[0057] Major effects of the embodiment of the present invention asdescribed above are as follows.

[0058] The use of a simplified polynomial compared to a complex discreteVolterra series minimizes computation complexity, a current predistortedsignal is generated using previous predistorted signals, and an accuratemodeling of the memory effects of a power amplifier enables appropriatelinearization of the power amplifier. Also, since I and Q signalcomponent errors are compensated for separately by use of complexpolynomial coefficients, each phase error is minimized independently.Therefore, the non-linearity of the power amplifier is effectivelycompensated for.

[0059] While the invention has been shown and described with referenceto a certain embodiment thereof, it will be understood by those skilledin the art that various changes in form and details may be made thereinwithout departing from the spirit and scope of the invention as definedby the appended claims.

What is claimed is:
 1. A polynomial predistorter for predistorting acomplex modulated baseband signal, providing the predistorted signal toa power amplifier, and compensating for the non-linear distortioncharacteristic of the power amplifier using complex vectormultiplication, comprising: a first complex multiplier for generatingfirst complex predistortion gains using a current input signal andcomplex polynomial coefficients, for in-phase (I) predistortion andquadrature-phase (Q) predistortion, the complex polynomial coefficientsbeing modeled on the inverse non-linear distortion characteristic of thepower amplifier, and multiplying the first complex predistortion gainsby I and Q signal components of the current input signal, respectively;at least one second complex multiplier for generating second complexpredistortion gains using the complex polynomial coefficients andprevious predistorted signals corresponding to the complex polynomialcoefficients, for the I predistortion and the Q predistortion, andmultiplying the second complex predistortion gains by I and Q signalcomponents of the previous predistorted signals, respectively; and asummer for generating a predistorted signal by summing outputs of thefirst and second complex multipliers and outputting the predistortedsignal to the power amplifier.
 2. The polynomial predistorter of claim1, wherein the complex polynomial coefficients are determined such thatthe predistorted signal is output to an input of an amplifier output. 3.The polynomial predistorter of claim 1, wherein the predistorted signalis calculated using d(n)=d _(i)(n)+jd _(q)(n)=x(n)E(c _(i) +jc _(q))x(n)=[x _(i)(n),x _(q)(n), x _(i)(n)|x(n)|,x _(q)(n)|x(n)|, . . . , x_(i)(n)|x(n)|^(P−1) , x _(q)(n)|x(n)|^(P−1) , d _(i)(n−1),d _(q)(n−1),d_(i)(n−1)|d(n−1)|,d _(q)(n−1)|d(n−1)|, . . . , d _(i)(n−1)|d(n−1)|^(P−1),d _(q)(n−1)|d(n−1)|^(P−1) , d _(i)(n−M),d _(q)(n−M),d_(i)(n−M)|d(n−M)|,d _(q)(n−M)|d(n−M)|, . . . , d _(i)(n−M)|d(n−M)|^(P−1),d _(q)(n−M)|d(n−M)|^(P−1)]c _(i) =[c _(ii,0,0) ,c _(iq,0,0) , . . . ,c_(ii,0,(P−1)) ,c _(iq,0,(P−1)) ,c _(ii,1,0) ,c _(iq,1,0) , . . . ,c_(ii,1,(P−1)) ,c _(iq,1,(P−1)) , . . . , c _(ii,M,0) ,c _(iq,M,0) , . .. ,c _(ii,M,(P−1)) ,c _(iq,M,(P−1))]^(T) c _(q) =[c _(qi,0,0) ,c_(qq,0,0) , . . . ,c _(qi,0,(P−1)) ,c _(qq,0,(P−1)) ,c _(qi,1,0) ,c_(qq,1,0) , . . . ,c _(qi,1,(P−1)) ,c _(qq,1,(P−1)) , . . . , c_(qi,M,0) ,c _(qq,M,0) , . . . ,c _(qi,M,(P−1)) ,c _(qq,M,(P−1))]^(T)where d(n) is the predistorted signal including an I signal componentd_(i)(n) and a Q signal component d_(q)(n), x(n) is the input signalincluding an I signal component x_(i)(n) and a Q signal componentx_(q)(n), c₁ is an I polynomial coefficient including c_(ii) and c_(iq)that affect x_(i)(n) and x_(q)(n), respectively, c_(q) is a Q polynomialcoefficient including c_(qi) and c_(qq) that affect x_(i)(n) andx_(q)(n), respectively, P is the order of the polynomial, and M is thenumber of previous signals to consider.
 4. The polynomial predistorterof claim 1, wherein each of the first and second complex predistortiongains includes an I complex predistortion gain and a Q complexpredistortion gain which are multiplied respectively by the I and Qsignal components of the input signal and the previous predistortedsignals.
 5. The polynomial predistorter of claim 4, wherein the firstcomplex predistortion gains are calculated using p=c _(ii,0,0) +c_(ii,0,1) |x(n)|+ . . . +c _(ii,0,(P−1)) |x(n)|^((P−1)) q=c _(iq,0,0) +c_(iq,0,1) |x(n)|+ . . . +c _(iq,0,(P−1)) |x(n)|^((P−1)) r=c _(qi,0,0) +c_(qi,0,1) |x(n)|+ . . . +c _(qi,0,(P−1)) |x(n)|^((P−1)) s=c _(qq,0,0) +c_(qq,0,1) |x(n)|+ . . . +c _(qq,0,(P−1)) |x(n)|^((P−1)) where x(n) isthe input signal, p and q are I predistortion gains by which the I and Qsignal components of the input signal are multiplied, r and s are Qpredistortion gains by which the I and Q signal components of the inputsignal are multiplied, c_(ii) and c_(iq) are I polynomial coefficientsthat affect the I and Q signal components of the input signal,respectively, c_(qi) and c_(qq) are Q polynomial coefficients thataffect the I and Q signal components of the input signal, respectively,P is the order of the polynomial, and M is the number of previoussignals to consider.
 6. The polynomial predistorter of claim 4, whereinthe second complex predistortion gains are calculated using p=c_(ii,m,0) +c _(ii,m,1) |d(n−m)|+ . . . +c_(ii,m,(P−1)) |d(n−m)|^((P−1))q=c _(iq,m,0) +c _(qi,m,1) |d(n−m)|+ . . . +c_(iq,m,(P−1))|d(n−m)|^((P−1)) r=c _(qi,m,0) +c _(qi,m,1) |d(n−m)|+ . . .+c_(qi,m,(P−1)) |d(n−m)|^((P−1)) s=c _(qq,m,0) +c _(qq,m,1) |d(n−m)|+ .. . +c_(qq,m,(P−1)) |d(n−m)|^((P−1)) where d(n-m) is an mth previouspredistorted signal, p and q are I predistortion gains by which the Iand Q signal components of the input signal are multiplied, r and s areQ predistortion gains by which the I and Q signal components of theinput signal are multiplied, c_(ii) and c_(iq) are I polynomialcoefficients that affect the I and Q signal components of the inputsignal, respectively, c_(qi) and c_(qq) are Q polynomial coefficientsthat affect the I and Q signal components of the input signal,respectively, P is the order of the polynomial, and M is the number ofprevious signals to consider.
 7. A polynomial predistorting method ofpredistorting a complex modulated baseband signal, providing thepredistorted signal to a power amplifier, and compensating for thenon-linear distortion characteristic of the power amplifier usingcomplex vector multiplication, comprising the steps of: generating firstcomplex predistortion gains using a current input signal and complexpolynomial coefficients, for in-phase (I) predistortion andquadrature-phase (Q) predistortion, the complex polynomial coefficientsbeing modeled on the inverse non-linear distortion characteristic of thepower amplifier, and multiplying the first complex predistortion gainsby I and Q signal components of the current input signal, respectively;generating second complex predistortion gains using the complexpolynomial coefficients and a predetermined number of previouspredistorted signals, for the I predistortion and the Q predistortion,and multiplying the second complex predistortion gains by I and Q signalcomponents of the previous predistorted signals, respectively; andgenerating a predistorted signal by summing outputs of the first andsecond complex multipliers and outputting the predistorted signal to thepower amplifier.
 8. The polynomial predistorting method of claim 7,wherein the complex polynomial coefficients are determined such that thepredistorted signal is output to an input of an amplifier output.
 9. Thepolynomial predistorting method of claim 7, wherein the predistortedsignal is calculated using d(n)=d _(i)(n)+jd _(q)(n)=x(n)E(c _(i) +jc_(q)) x(n)=[x _(i)(n),x _(q)(n), x _(i)(n)|x(n)|,x _(q)(n)|x(n)|, . . ., x _(i)(n)|x(n)|^(P−1) , x _(q)(n)|x(n)|^(P−1) , d _(i)(n−1),d_(q)(n−1),d _(i)(n−1)|d(n−1)|,d _(q)(n−1)|d(n−1)|, . . . , d_(i)(n−1)|d(n−1)|^(P−1) ,d _(q)(n−1)|d(n−1)|^(P−1) , d _(i)(n−M),d_(q)(n−M),d _(i)(n−M)|d(n−M)|,d _(q)(n−M)|d(n−M)|, . . . , d_(i)(n−M)|d(n−M)|^(P−1) ,d _(q)(n−M)|d(n−M)|^(P−1)]c _(i) =[c _(ii,0,0),c _(iq,0,0) , . . . ,c _(ii,0,(P−1)) ,c _(iq,0,(P−1)) ,c _(ii,1,0) ,c_(iq,1,0) , . . . ,c _(ii,1,(P−1)) ,c _(iq,1,(P−1)) , . . . , c_(ii,M,0) ,c _(iq,M,0) , . . . ,c _(ii,M,(P−1)) ,c _(iq,M,(P−1))]^(T) c_(q) =[c _(qi,0,0) ,c _(qq,0,0) , . . . ,c _(qi,0,(P−1)) ,c_(qq,0,(P−1)) ,c _(qi,1,0) ,c _(qq,1,0) , . . . ,c _(qi,1,(P−1)) ,c_(qq,1,(P−1)) , . . . , c _(qi,M,0) ,c _(qq,M,0) , . . . ,c_(qi,M,(P−1)) ,c _(qq,M,(P−1))]^(T) where d(n) is the predistortedsignal including an I signal component d_(i)(n) and a Q signal componentd_(q)(n), x(n) is the input signal including an I signal componentx_(i)(n) and a Q signal component x_(q)(n), c_(i) is an I polynomialcoefficient including c_(ii) and c_(iq) that affect x_(i)(n) andx_(q)(n), respectively, c_(q) is a Q polynomial coefficient includingc_(qi) and c_(qq) that affect x_(i)(n) and x_(q)(n), respectively, P isthe order of the polynomial, and M is the number of previous signals toconsider.
 10. The polynomial predistorting method of claim 7, whereineach of the first and second complex predistortion gains includes an Icomplex predistortion gain and a Q complex predistortion gain which aremultiplied respectively by the I and Q signal components of the inputsignal and the previous predistorted signals.
 11. The polynomialpredistorting method of claim 10, wherein the first complexpredistortion gains are calculated using p=c _(ii,0,0) +c _(ii,0,1)|x(n)|+ . . . +c _(ii,0,(P−1)) |x(n)|^((P−1)) q=c _(iq,0,0) +c _(iq,0,1)|x(n)|+ . . . +c _(iq,0,(P−1)) |x(n)|^((P−1)) r=c _(qi,0,0) +c _(qi,0,1)|x(n)|+ . . . +c _(qi,0,(P−1)) |x(n)|^((P−1)) s=c _(qq,0,0) +c _(qq,0,1)|x(n)|+ . . . +c _(qq,0,(P−1)) |x(n)|^((P−1)) where x(n) is the inputsignal, p and q are I predistortion gains by which the I and Q signalcomponents of the input signal are multiplied, r and s are Qpredistortion gains by which the I and Q signal components of the inputsignal are multiplied, c_(ii) and c_(iq) are I polynomial coefficientsthat affect the I and Q signal components of the input signal,respectively, c_(qi) and c_(qq) are Q polynomial coefficients thataffect the I and Q signal components of the input signal, respectively,P is the order of the polynomial, and M is the number of previoussignals to consider.
 12. The polynomial predistorting method of claim10, wherein the second complex predistortion gains are calculated usingp=c _(ii,m,0) +c _(ii,m,1) |d(n−m)|+ . . . +c_(ii,m,(P−1))|d(n−m)|^((P−1)) q=c _(iq,m,0) +c _(qi,m,1) |d(n−m)|+ . . .+c_(iq,m,(P−1)) |d(n−m)|^((P−1)) r=c _(qi,m,0) +c _(qi,m,1) |d(n−m)|+ .. . +c_(qi,m,(P−1)) |d(n−m)|^((P−1)) s=c _(qq,m,0) +c _(qq,m,1)|d(n−m)|+ . . . +c_(qq,m,(P−1)) |d(n−m)|^((P−1)) where d(n-m) is an mthprevious predistorted signal, p and q are I predistortion gains by whichthe I and Q signal components of the input signal are multiplied, r ands are Q predistortion gains by which the I and Q signal components ofthe input signal are multiplied, c_(ii) and c_(iq) are I polynomialcoefficients that affect the I and Q signal components of the inputsignal, respectively, c_(qi) and c_(qq) are Q polynomial coefficientsthat affect the I and Q signal components of the input signal,respectively, P is the order of the polynomial, and M is the number ofprevious signals to consider.